Longitudinal Data Analysis and Time Series Commons^™

Modeling Volatility Of Financial Time Series Using Arc Length, Benjamin H. Hoerlein

Electronic Theses and Dissertations

This thesis explores how arc length can be modeled and used to measure the risk involved with a financial time series. Having arc length as a measure of volatility can help an investor in sorting which stocks are safer/riskier to invest in. A Gamma autoregressive model of order one(GAR(1)) is proposed to model arc length series. Kernel regression based bias correction is studied when model parameters are estimated using method of moment procedure. As an application, a model-based clustering involving thirty different stocks is presented using k-means++ and hierarchical clustering techniques.